Currently, it's not possible to set up HTML-based auto-reply messages on shared or resource mailboxes, as you cannot directly log on to OWA to set the message. Through Powershell, you can do this quite easily.

First, create two HTML-files containing your internal and external message. You do not have to specify the <html> and <body> tags. Save these to a convenient location. Be sure to save them as regular text files, with extension .txt.

Next, log on to Exchange Online management shell.

cd to the location of the two message files, and load them to variables: